Strict Henselization

Summary

The strict Henselization of a local ring $R$ is a Henselian local ring over $R$. Its residue field is a separable closure of the residue field of $R$. It is universal among local maps from $R$ to strictly Henselian local rings, that is, Henselian local rings with a separably closed residue field. It refines the Henselization, which keeps the residue field unchanged. In algebraic geometry the strict Henselizations of the local rings of a scheme are the stalks of its structure sheaf for the étale topology.